Multiple choice

The age of Sitamma 10 years ago was thrice the age of Radha. 10 years hence, Sitamma's age will be twice that of Radha. What is the ratio of the present ages of Radha and Sitamma?

  1. 3 : 7

  2. 3 : 1

  3. 2 : 1

  4. None of these
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A Correct answer
Explanation

Let S and R be present ages. (S-10) = 3(R-10) => S-10 = 3R-30 => S = 3R-20. (S+10) = 2(R+10) => S+10 = 2R+20 => S = 2R+10. 3R-20 = 2R+10 => R = 30. S = 2(30)+10 = 70. Ratio R:S = 30:70 = 3:7.

AI explanation

Let the present ages of Sitamma and Radha be S and R respectively. Ten years ago, the equation was S minus 10 equals 3 multiplied by (R minus 10), which simplifies to S equals 3R minus 20. Ten years hence, the equation is S plus 10 equals 2 multiplied by (R plus 10), which simplifies to S equals 2R plus 10. Setting the two equations equal gives 3R minus 20 equals 2R plus 10, meaning R equals 30; substituting this back yields S equals 70, making their ratio 30 to 70, which simplifies to 3 to 7.

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